DNA Splicing Systems based on Post Systems (original) (raw)
DNA splicing systems (or simply splicing systems) are a new type of generative mechanisms for modeling DNA recombination behaviors, initiated by Tom Head's seminal paper (8]). For this reason, splicing systems are sometimes called Head systems (H systems), and a number of extensive work on this exciting subject have already been reported by many authors. Among others, Paun's recent result shows that extended H systems with nite sets of axioms and regular sets of rules exactly characterize the recursively enumerable languages, thus having the full power of Turing machines (13]). Also, more recently it is shown that there is a universal extended H system analogous to a universal Turing machine (4]). This paper concerns further formal study on the generative powers of extended H systems. First, using a classical result by Post which characterizes the recursively enumerable languages in terms of his Post Normal systems, we establish several new characterizations of extended H systems which not only allow us to have very simple alternative proof methods for the previous results mentioned above, but also give a new insight into the relationships between families of extended H systems. In fact, we show a kind of normal form for extended H systems exactly characterizing the class of regular languages. We also show a new representation result for the family of context-free languages in terms of extended H systems, which may shed new light on the relationship between the classical formal language theory and this new theory of splicing DNA languages.
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